Question:
How much loan did Susan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7062.5 to clear it?
Correct Answer
$5650
Solution And Explanation
Solution
Given,
Amount (A) = $7062.5
Rate of Simple Interest (R) = 5%
Time (T) = 5 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$7062.5 = P (1 + 5% × 5)
⇒ $7062.5 = P (1 + 5/100 × 5)
⇒ $7062.5 = P (1 + 5 × 5/100)
⇒ $7062.5 = P (1 + 25/100)
⇒ $7062.5 = P (100 + 25/100)
⇒ $7062.5 = P × 125/100
⇒ P × 125/100 = $7062.5
⇒ P = 7062.5/125/100
⇒ P = 7062.5 × 100/125
⇒ P = 7062.5 × 100/125
⇒ P = 706250/125
⇒ P = $5650
Thus, the sum borrowed (P) = $5650 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7062.5, then the Principal = 100/125 × 7062.5
= 100 × 7062.5/125
= 706250/125
= 5650
Thus, Principal = $5650
Thus, the sum borrowed = $5650 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?
(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.
(7) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?
(10) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?